HeightsHeights 

of statistics students were obtained by a teacher as part of an experiment conducted for the class. The last digit of those 

heightsheights 

are listed below. Construct a frequency distribution with 10 classes. Based on the​ distribution, do the 

heightsheights 

appear to be reported or actually​ measured? What can be said about the accuracy of the​ results?

00 

00 

00 

00 

00 

00 

00 

00 

00 

11 

22 

22 

33 

33 

44 

44 

55 

55 

55 

55 

55 

55 

55 

55 

55 

55 

66 

88 

88 

88 

99 
  
Question content area bottom

Part 1

Complete the frequency distribution below.

Last digit

Frequency

Last digit

Frequency

0

enter your response here

5

enter your response here

1

enter your response here

6

enter your response here

2

enter your response here

7

enter your response here

3

enter your response here

8

enter your response here

4

enter your response here

9

enter your response here

​(Type integers or​ decimals.)

Let's start by organizing the data into a frequency distribution. The last digits of the heights given are:

- \(0: 9\) occurrences
- \(1: 1\) occurrence
- \(2: 2\) occurrences
- \(3: 2\) occurrences
- \(4: 2\) occurrences
- \(5: 10\) occurrences
- \(6: 1\) occurrence
- \(7: 0\) occurrences
- \(8: 3\) occurrences
- \(9: 1\) occurrence

Now, let's complete the frequency distribution table:

| **Last digit** | **Frequency** |
|----------------|---------------|
| 0              | 9             |
| 1              | 1             |
| 2              | 2             |
| 3              | 2             |
| 4              | 2             |
| 5              | 10            |
| 6              | 1             |
| 7              | 0             |
| 8              | 3             |
| 9              | 1             |

### Analysis:

1. **Reporting or Measuring**: 
   - The digit "0" occurs disproportionately often, and "5" also has a high frequency. These digits are often used when people round numbers. Additionally, "7" never occurs, which is unusual if the data were truly measured.
   - **Conclusion**: The heights appear to be reported rather than actually measured.

2. **Accuracy**:
   - Since people often round to the nearest 0 or 5, the distribution suggests that the measurements might not be very accurate. Instead of precise measurements, these numbers might reflect estimates or rounded figures.

### Questions to Consider:
1. How would the frequency distribution change if the data were measured more accurately?
2. What statistical tests can confirm if the data are rounded or actually measured?
3. How does the rounding of data affect statistical analysis outcomes?
4. What is the impact of biased data on the validity of research conclusions?
5. Can you identify other patterns in reported vs. measured data?

### Tip:
When collecting data, it's crucial to ensure accuracy and precision to avoid introducing bias that can affect the outcome of statistical analysis.

Learn how to construct a frequency distribution for heights data with a detailed example. Analyze the distribution to determine if heights were reported or actually measured based on the frequency of last digits. Suitable for high school students studying statistics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation